|
| | | | |
| | | |
| Stat |
Members: 3669
Articles: 2'599'751
Articles rated: 2609
24 March 2025 |
|
| | | | |
|
Article overview
| |
|
|
Fitting Matérn Smoothness Parameters Using Automatic Differentiation | | Christopher J. Geoga
; Oana Marin
; Michel Schanen
; Michael L. Stein
; | | Date: |
1 Jan 2022 | | Abstract: | The Matérn covariance function is ubiquitous in the application of Gaussian
processes to spatial statistics and beyond. Perhaps the most important reason
for this is that the smoothness parameter $
u$ gives complete control over the
mean-square differentiability of the process, which has significant
implications about the behavior of estimated quantities such as interpolants
and forecasts. Unfortunately, derivatives of the Matérn covariance function
with respect to $
u$ require derivatives of the modified second-kind Bessel
function $mathcal{K}_
u$ with respect to $
u$. While closed form expressions
of these derivatives do exist, they are prohibitively difficult and expensive
to compute. For this reason, many software packages require fixing $
u$ as
opposed to estimating it, and all existing software packages that attempt to
offer the functionality of estimating $
u$ use finite difference estimates for
$partial_
u mathcal{K}_
u$. In this work, we introduce a new implementation
of $mathcal{K}_
u$ that has been designed to provide derivatives via
automatic differentiation, and whose resulting derivatives are significantly
faster and more accurate than using finite differences. We provide
comprehensive testing for both speed and accuracy and provide a motivating
demonstration in which maximum likelihood estimation via second order
optimization using finite difference approximations for derivatives with
respect to $
u$ gives completely incorrect answers. | | Source: | arXiv, 2201.00090 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
|
| |
|
|
|
REGISTER